I think some of it depends on how much context you still have. For me, a lot of the people I knew back home are here. A lot of them remember me for all of the things I was before I came here, even if those things aren't part of the life I'm living now. Being a billionaire, running a company, leading a team of superheroes, accidentally beaning Rupert Murdoch at a charity golf tournament. People know those things about me, know me through or because of those things, and so there are still ripples of that. I still feel like that person, temporarily put out by circumstances.
If it were just me here, alone, without anyone from home? I don't know if I'd still feel like myself. That life and all of those things I hang my hat on would probably feel very distant. I imagine there are underlying things that would be the same - personality traits, and the like. I've definitely run away from myself enough times to know that there are core attributes I can't really escape from. But I think the way I saw myself would fade into something else over time. I'm not sure what it would be.